How to make continuous movement of a windshield wiper with Logic Bricks?
Animate your windshield wipers moving back and forth, just one complete cycle.


Then add an Action actuator to play it. Make sure to set the EndFrame to match the length of your animation. Change the Action Playback Type from Play to Loop Stop, and choose the name of the action (by default is is named "Object name + Action")

The trick here is you want the keyboard sensor triggering a Property actuator, not the action actuator, then the property will trigger the action.
Add a game property, a boolean named "wipers" leave it false by default (blank checkbox).

Connect the keyboard sensor to a Property actuator, set it's mode to Toggle and choose the property you just created (wipers).

Now back on the sensor side, add a Property sensor, connect it to the action actuator. Set like so: Evaluation Type to be Equal, Property to be your game property (wipers), and the Value to be "True".

The full logic setup looks like this.